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# In the figure above, the area of square region PRTV is 81, and the rat

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Manager
Joined: 06 Feb 2010
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In the figure above, the area of square region PRTV is 81, and the rat  [#permalink]

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Updated on: 16 Oct 2018, 01:29
5
2
00:00

Difficulty:

25% (medium)

Question Stats:

81% (02:14) correct 19% (03:00) wrong based on 209 sessions

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In the figure above, the area of square region PRTV is 81, and the ratio of the area of square region XSTU to the area of square region PQXW is 1 to 4. What is the length of segment RS?

A. 5
B. 5.5
C. 6
D. 6.5
E. 7

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Untitled.png [ 7.1 KiB | Viewed 6452 times ]

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Originally posted by monirjewel on 09 Nov 2010, 01:08.
Last edited by Bunuel on 16 Oct 2018, 01:29, edited 2 times in total.
Renamed the topic and edited the question.
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Re: In the figure above, the area of square region PRTV is 81, and the rat  [#permalink]

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09 Nov 2010, 01:17
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2

In the figure above, the area of square region PRTV is 81, and the ratio of the area of square region XSTU to the area of square region PQXW is 1 to 4. What is the length of segment RS?
A. 5
B. 5.5
C. 6
D. 6.5
E. 7

As the area of square region PRTV is 81 then $$RT^2=81$$ --> $$RT=9$$;

The area of square region $$PQXW=QX^2=RS^2$$ and the area of square region $$XSTU=ST^2=(9-RS)^2$$;

Given: $$\frac{(9-RS)^2}{RS^2}=\frac{1}{4}$$ --> $$\frac{9-RS}{RS}=\frac{1}{2}$$ --> $$RS=6$$.

Or: as the ratio of the areas of squares is the square of the ratio of their sides then $$\frac{ST}{RS}=\frac{9-RS}{RS}=\frac{1}{2}$$ --> $$RS=6$$.
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Manager
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Location: Zürich, Switzerland
Re: In the figure above, the area of square region PRTV is 81, and the rat  [#permalink]

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09 Nov 2010, 03:22
(ST)^2/(QX)^2 = 1/4
So, QX=RS=2ST
since- RT=9(total area of PRTV=81), RT= 3ST.
So ST=3 and RS=6

Manager
Joined: 20 Apr 2010
Posts: 187
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Re: In the figure above, the area of square region PRTV is 81, and the rat  [#permalink]

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09 Nov 2010, 08:16
1
If the area is 1:4 than the sides will be 1:2
since the total length is 9 (RS+ST) hence it is (3+6) since RS is the Bigger in length therefore,RS = 6
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Re: In the figure above, the area of square region PRTV is 81, and the rat  [#permalink]

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05 Jan 2011, 22:51
I don't agree with the answer "D" - I think it's C

PRTV is a square, with area of 81 => RT = 9

RT = RS + ST = 9

RS^2 = 4ST ^ 2
=> RS = 2ST

=>3ST = 9
=> ST = 3

=> RS = 6

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Re: In the figure above, the area of square region PRTV is 81, and the rat  [#permalink]

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06 Jan 2011, 00:33
RT=9 since area of square is 81

Let RS=x and ST=9-x

Ratio of the area of squares is 1:4
Hence x^2 = 4 (9-x)^2
Hence x = 2(9-x)
3x = 18 ... x=6

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Re: In the figure above, the area of square region PRTV is 81, and the rat  [#permalink]

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16 Oct 2018, 01:29
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Re: In the figure above, the area of square region PRTV is 81, and the rat   [#permalink] 16 Oct 2018, 01:29
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